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150°

Warm Up 1. Find the measure of exterior  DBA of BCD , if m DBC = 30°, m C = 70°, and mD = 80°. 2. What is the complement of an angle with measure 17°? 3. How many lines can be drawn through N parallel to MP ? Why?. 150°. 73°. 1; Parallel Post.

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150°

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  1. Warm Up 1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°. 2. What is the complement of an angle with measure 17°? 3. How many lines can be drawn through N parallel to MP? Why? 150° 73° 1; Parallel Post.

  2. An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem

  3. Find mXYZ. mXYZ + mYZX + mZXY = 180° mXYZ + 40+ 62= 180 mXYZ + 102= 180 mXYZ = 78°

  4. 118° Find mYWZ. Step 1Find mWXY. mYXZ + mWXY = 180° 62 + mWXY = 180 mWXY = 118° Step 2Find mYWZ. mYWX + mWXY + mXYW = 180° mYWX + 118+ 12= 180 mYWX + 130= 180 mYWX = 50°

  5. You Try: mMJK + mJKM + mKMJ = 180° mMJK + 104+ 44= 180 mMJK + 148= 180 mMJK = 32°

  6. A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

  7. One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? Let the acute angles be A and B, with mA = 2x°. mA + mB = 90° 2x+ mB = 90 mB = (90 – 2x)°

  8. You Try: The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle? Let the acute angles be A and B, with mA = 63.7°. mA + mB = 90° 63.7 + mB = 90 mB = 26.3°

  9. The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure. Exterior Interior

  10. An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. 4 is an exterior angle. Exterior Interior 3 is an interior angle.

  11. Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle. 4 is an exterior angle. The remote interior angles of 4 are 1 and 2. Exterior Interior 3 is an interior angle.

  12. Find mB. mA + mB = mBCD 15 + 2x + 3= 5x – 60 2x + 18= 5x – 60 78 = 3x 26 = x mB = 2x + 3 = 2(26) + 3 = 55°

  13. You Try: Find mACD. mACD = mA + mB 6z – 9 = 2z + 1+ 90 6z – 9= 2z + 91 4z = 100 z = 25 mACD = 6z – 9 = 6(25) – 9 = 141°

  14. Find mK and mJ. K  J mK = mJ 4y2= 6y2 – 40 –2y2 = –40 y2 = 20 So mK = 4y2 = 4(20) = 80°. Since mJ = mK,mJ =80°.

  15. You Try! Find mP and mT. P  T mP = mT 2x2= 4x2 – 32 –2x2 = –32 x2 = 16 So mP = 2x2 = 2(16) = 32°. Since mP = mT,mT =32°.

  16. 1 3 33 ° 2 3 Lesson Quiz: Part I 1. The measure of one of the acute angles in a right triangle is 56 °. What is the measure of the other acute angle? 2. Find mABD. 3. Find mN and mP. 124° 75°; 75°

  17. Lesson Quiz: Part II 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store? 30°

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